Deformable structures collapsible tubular mast (ctm)

ABSTRACT

A deformable device includes a deformable beam or hinge having an extended state, a flattened state, and a rolled state if a beam, where a stiffness and strength in the extended state is greater than a different stiffness and strength in the flattened state, the deformable beam or the hinge deformable along a long axis. An end face cross section transverse to the long axis includes a first periodic curved member which defines at least two shaped curves. A second periodic curved member defines at least two shaped curves. The second periodic curved member is mechanically coupled to the first periodic curved member at respective ends of the end face cross section. The first arc length of the first periodic curved member and the second arc length of the second periodic curved member are of about a same arc length.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of now allowed U.S. patent application Ser. No. 16/724,806, DEFORMABLE STRUCTURES COLLAPSIBLE TUBULAR MAST (CTM), filed on Dec. 23, 2019, which application is a continuation-in-part of U.S. patent application Ser. No. 15/959,815, filed on Apr. 23, 2018, DEFORMABLE STRUCTURES, now U.S. Pat. No. 10,526,785 and claims priority to and the benefit of U.S. provisional patent application Ser. No. 62/490,289 now expired, DEFORMABLE STRUCTURES, filed Apr. 26, 2017 and PCT Application No. PCT/US2018/029348, filed Apr. 25, 2018, DEFORMABLE STRUCTURES published as WO2018200667 A1, all of which applications are incorporated herein by reference in their entirety.

FIELD OF THE APPLICATION

The application relates to deformable structures and particularly to deformable beams and deformable hinges.

BACKGROUND

Deformable structures are structures that can dramatically change shape.

SUMMARY

A deformable device includes a deformable beam or hinge having an extended state, a flattened state, and a rolled state if a beam, where a stiffness and strength of the deformable beam or the hinge in the extended state is greater than a different stiffness and strength of the deformable beam or the hinge in the flattened state, the deformable beam or the hinge deformable along a long axis. An end face cross section of the deformable beam or the hinge transverse to the long axis includes a first periodic curved member which defines at least two shaped curves. The first periodic curved member includes a first arc length. A second periodic curved member defines at least two shaped curves. The second periodic curved member includes a second arc length. The second periodic curved member is mechanically coupled to the first periodic curved member at respective ends of the end face cross section. The first arc length and the second arc length are of about a same arc length.

The first arc length and the second arc length are of a substantially same arc length. The first arc length and the second arc length can include a substantially same arc length between both joined curve ends. The first arc length and the second arc length can include a substantially same arc length between both joined curve ends of the end face cross section.

The first periodic curved member can include at least two about C curved members. The second periodic curved member can include at least two about C curved members. The first periodic curved member can include at least two about C curved members and the second period curved member can include at least two about C curved members.

At least one of the first periodic curved member and the second periodic curved member cam include an additional different shape.

At least one of the first periodic curved member and the second periodic curved member can include a [B/UD@0/B] fibre structure or a [B/UD@0] or a [B] fibre structure.

At least one member of the deformable device can include at least one cut out along a length of the member.

The first periodic curved member can include a different thickness relative to the second periodic curved member.

At least one of the first periodic curved member and the second periodic curved member can include a variation in thickness across either or both of the first periodic curved member and the second periodic curved member.

The foregoing and other aspects, features, and advantages of the application will become more apparent from the following description and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the application can be better understood with reference to the drawings described below, and the claims. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles described herein. In the drawings, like numerals are used to indicate like parts throughout the various views.

FIG. 1 shows a drawing showing basic end view cross section classes of exemplary deformable structures;

FIG. 2A shows a cross section view of a DubC Boom;

FIG. 2B shows an isometric view of an opened DubC Boom;

FIG. 2C shows an isometric view of a flattened DubC Boom;

FIG. 2D shows an isometric view of a rolled DubC Boom;

FIG. 3A shows a cross section view of a DubC Hinge;

FIG. 3B shows an isometric view of an opened DubC Hinge;

FIG. 3C shows an isometric view of a flattened DubC Hinge;

FIG. 3D shows an isometric view of a rolled DubC Hinge;

FIG. 4A shows a cross section view of a MidC Hinge;

FIG. 4B shows an isometric view of an opened MidC Hinge;

FIG. 4C shows an isometric view of a flattened MidC Hinge;

FIG. 4D shows an isometric view of a rolled MidC Hinge;

FIG. 5A shows a cross section view of a TriC Hinge;

FIG. 5B shows an isometric view of an opened TriC Hinge;

FIG. 5C shows an isometric view of a flattened TriC Hinge;

FIG. 5D shows an isometric view of a rolled TriC Hinge;

FIG. 6A shows a cross section view of a TriC Flat Boom;

FIG. 6B shows an isometric view of an opened TriC Flat Boom;

FIG. 6C shows an isometric view of a flattened TriC Flat Boom;

FIG. 6D shows an isometric view of a rolled TriC Flat Boom;

FIG. 7A shows a cross section view of a Z Boom;

FIG. 7B shows an isometric view of an opened Z Boom;

FIG. 7C shows an isometric view of a flattened Z Boom;

FIG. 7D shows an isometric view of a rolled Z Boom;

FIG. 8A shows a cross section view of a Z Hinge;

FIG. 8B shows an isometric view of an opened Z Hinge;

FIG. 8C shows an isometric view of a flattened Z Hinge;

FIG. 8D shows an isometric view of a rolled Z Hinge;

FIG. 9 shows another drawing showing end view cross section classes of exemplary Z Boom deformable structures;

FIG. 10 shows another drawing showing end view cross section classes of exemplary C Boom deformable structures;

FIG. 11 shows yet another drawing showing end view cross section classes of exemplary C Boom deformable structures;

FIG. 12 shows yet another drawing showing end view cross section classes of exemplary C Boom deformable structures;

FIG. 13 shows yet another drawing showing end view cross section classes of exemplary TriC variation, DubC Variation, and other variation deformable structures;

FIG. 14 shows exemplary DubC end modifications;

FIG. 15 shows exemplary MidC end modifications;

FIG. 16 shows exemplary TriC end modifications;

FIG. 17 shows exemplary Z Boom end modifications;

FIG. 18A shows end view of a DubC deformable structure having a thicker center relative to the tips;

FIG. 18B shows end view of a DubC deformable structure having thicker tips relative to the center portion;

FIG. 19A shows an end view of a DubC deformable structure with a [B/UD@0/B] central portion and [B] ends;

FIG. 19B shows an end view of a DubC deformable structure with a [UD@0/B/UD@0] central portion and [B] ends;

FIG. 19C shows an end view of a DubC deformable structure with a [UD@0/B/UD@0] central portion and [B/UD@0] ends;

FIG. 19D shows an end view of a DubC deformable structure of substantially all [B/UD@0/B];

FIG. 19E shows an end view of a DubC deformable structure of substantially all [UD@0/B/UD@0];

FIG. 20A shows a drawing of MidC deformable structure with a thicker center relative to the tips;

FIG. 20B shows a drawing of MidC deformable structure with thicker tips relative to the center;

FIG. 21A shows an end view of a MidC center member [B/UD@0/B] and curved members of [B];

FIG. 21B shows an end view of a MidC deformable structure substantially all of [B/UD@0/B];

FIG. 21C shows an end view of a MidC deformable structure, with a [B/UD@0/B] central member and curved members of [B/UD@0/B];

FIG. 22A shows an end view of a TriC deformable structure with a thicker main circle portion relative to the other portions of the TriC structure;

FIG. 22B shows an end view of a TriC deformable structure with noted thicker regions relative to the other portions of the TriC structure;

FIG. 22C shows an end view of a TriC deformable structure with different noted thicker regions relative to the other portions of the TriC structure;

FIG. 23A shows an end view of a TriC deformable structure with a [B/UD@0/B] main circle portion, where the other portions are [B];

FIG. 23B shows an end view of a [B] type TriC deformable structure with a [B/UD@0/B] main circle portion, where the other portions are [B];

FIG. 23C shows an end view of a TriC deformable structure with a [B] main circle portion, where the other portions are [B/UD@0];

FIG. 24A shows a drawing of Z Boom deformable structure with thicker flats relative to the center curved portion;

FIG. 24B shows a drawing of Z Boom deformable structure with noted thicker regions relative to the other portions;

FIG. 25 shows drawings of various Z Boom fiber orientations;

FIG. 26 shows a drawing of another exemplary MidC deformable structure with double opposing portions;

FIG. 27A shows a drawing of yet another exemplary TriC deformable structure with about flat sections;

FIG. 27B shows a drawing of yet another exemplary TriC deformable structure with about circular sections;

FIG. 27C shows a drawing of yet another exemplary TriC deformable structure with near or about circular sections;

FIG. 27D shows a drawing of yet another exemplary TriC deformable structure with an outward facing jointed member ends;

FIG. 28 shows yet another drawing showing end view cross section classes of exemplary TriC variation, DubC Variation, and other variation deformable structures;

FIG. 29A is a drawing showing an exemplary CTM boom;

FIG. 29B is a drawing showing a magnified view of an end of the CTM boom of FIG. 29B;

FIG. 29C is a drawing showing a magnified view of a portion of the CTM boom of FIG. 29B;

FIG. 29C shows one exemplary flat wall;

FIG. 29D is a drawing showing an end section view of the CTM boom of FIG. 209A;

FIG. 30 shows a cross section of an exemplary CTM boom using a flat-back C curve;

FIG. 31 shows an exemplary CTM boom using a flat-back C curve with an alternative truss pattern;

FIG. 32 shows another exemplary CTM boom using a flat-back C curve with a diagonal truss;

FIG. 33 shows yet another exemplary CTM boom using a flat-back C curve with truss pattern;

FIG. 34 shows yet another exemplary CTM boom using a flat-back C curve with truss pattern;

FIG. 35 shows a top view of the CTM boom 3400 of FIG. 34;

FIG. 36 is a drawing showing an isometric view of exemplary four sided CTM frame;

FIG. 37 is a drawing showing a top view of the CTM frame of FIG. 36;

FIG. 38 is another top view of another CTM frame similar to FIG. 36 showing corner sections and a supporting sheet material;

FIG. 39 is a drawing showing an exemplary frame based on a H configuration architecture;

FIG. 40 is a drawing showing an exemplary frame based on a radial 3 configuration architecture;

FIG. 41 is a drawing showing an exemplary frame based on a radial 4 configuration architecture;

FIG. 42 is a drawing showing an exemplary curved truss member;

FIG. 43 is a drawing showing a mid-section cut-away of the curved truss member of FIG. 42;

FIG. 44 is a drawing showing an end view of the sectional cut-away view of FIG. 43;

FIG. 45 is a drawing showing an exemplary CTM boom using curved diagonal truss members; and

FIG. 46 is a drawing showing a cross section view of the CTM boom of FIG. 45.

DETAILED DESCRIPTION

DEFINITIONS: The phrase “end modification” as used herein, describes modifications of the physical end of a structure.

Axial stiffness refers to a stiffness along the structure long axis. In general, extended states are stiffer with respect to multiple axes (axes include torsion, two bending axes, two sheer, and axial).

Truss member—A truss member mechanically couples at two end points, hereinbelow generally between a vertex structure and a joining portion of a beam, mast, and/or boom, where the truss member includes an element about perpendicular to the long axis of a beam or hinge as a batten truss member, or as a diagonal truss member. Truss members can be about flat, or rounded, such as analogous to the curved metal tape of a tape measure or tape spring.

Plurality—common meaning, more than one, or at least two.

Deformable structures can dramatically change shape. While all structures are deformable to some extent, structures of this Application, change shape so dramatically that the original form of the structure can be difficult to recognize in the deformed shape. The shape change is designed to allow the structure to meet one set of desired requirements in one shape, and another set of desired requirements in another shape. A common example of a prior art deformable structure is an elastic tape-spring hinge that allows a structure to fold and compactly package for mobility and subsequent unfolding and locking into a stiff and strong structure.

Applications requiring structures that can change shape are vast and include, for example, sun shades, airfoils, awnings, retractable roofs, deployable space structures, etc. The present invention relates to reconfigurable hinges and beams. They can form elements of more complex reconfigurable structures, such as a truss.

Structural members which can be flattened and rolled are described in detail hereinbelow. In lengths from about equal to the flattened width to 10 times the flattened width, the structural member can be used as a self-locking hinge (a deformable hinge). In lengths from about 4 times the flattened width to 1,000 times the flattened width, the structural member can be used as a furlable beam (a deformable beam). The furlable beam can be flattened in one or more directions, reducing the stiffness and strength of the member. The furlable beam can then be rolled to compactly package it.

A deformable beam having an extended state, a flattened state, and a rolled state. An axial stiffness of the deformable beam in the extended state is greater than an axial stiffness in the flattened state. A deformable hinge has two states including an extended state, and a folded state. An axial stiffness of the deformable hinge in the extended state is greater than an axial stiffness in the folded state.

New shapes of deformable structures, new deformable structures, and new applications for the deformable structures are described in this Application.

In some embodiments, the structural member is beam-like and has a longitudinal axis extending the length of the beam. In one exemplary embodiment, the beam cross section is primarily prismatic, primarily tapered, or any combination thereof.

FIG. 1 shows a drawing showing exemplary basic end view cross section classes of a DubC Boom, a DubC Hinge, a MidC, TriC Boom, a TriC Hinge, a Z Boom, and a Z Hinge.

The DubC end face structure (cross section) includes two about circular members joined back to back at about a center portion of the two circular portions. Each of the two about circular members typically include between about a quarter about circle to about a half about circle shape. In other words, the curved portions are joined back to back at about a center portion of a curve.

The MidC end face (cross section) structure includes two curved members, each of the two curved members are joined at about the ends of the curves, and at the end of a substantially center substantially flat or straight member. In other words, the end face cross section structure includes a plurality of curved members having a curve end and an opposite curve end, each of the curve ends are joined together, and each of the opposite curved ends are non-joined tips.

The TriC end face (cross section) structure includes an about “C” shape as an about circular member ranging from about a quarter about circle to nearly or about a full circle joined to at both ends of the about circular portion to a curve member which extends between both ends of the about circular member. The curve which extends between both ends of the about circular member can include a desired curve shape with about two or more about “C” shapes. For example, the curve which extends between both ends of the about circular member can include an about sine curve shape (the “sine shape” to convey a sense of a repeating or periodic waveform, however, typically, more “C” shaped), such as including an about sine curve shape (e.g. successive “C” shapes of alternating orientation) of, for example, one and one-half cycles of a sine curve (e.g. from sine 0° to sine 540°). Each of the curved portions are joined at about a curve end.

TriC deformable structures, and C booms or hinges more generally, are one example of typically “closed” curves. In a closed curve deformable structure, the cross section or end view presents at least one continuous line which closes on itself. In order to properly transition to a flattened state or rolled state, curves which run substantially parallel to each other in the longitudinal direction (e.g. along a beam) should have the same arc length between joined curve ends. With substantially the same arc length between joined curve ends, when the deformable structure flattens, there should be substantially no wrinkles or distortion of the surfaces of either of the curved sections. If the arc lengths are significantly different, one or both of the structures will wrinkle or otherwise be damaged, probably irreversibly damaged, such as at the joints, when the structure is made flat.

In more detail, an end face cross section of the deformable beam TriC type deformable structure, includes a main C curved member 501 which defines an about circular shape of an arc ranging between about a quarter arc and a substantially full circle. The main C curved member has a first main C curved member end 511 and a second main C curved member end 513. A periodic C curved member 509 defines at least two about C shaped curves (507, 508). The periodic C curved member 509 has a first periodic C curved member end 517 mechanically coupled to the first main C curved member end 511, and a second periodic C curved member end 519 mechanically coupled to the second main C curved member end 513.

In typical embodiments, while parts of the periodic C curved member 509 can extend outside of the main C curved member 501, at least one of the first periodic C curved member end 517 is joined to the first main C curved member end 511 inside of the main C curved member 501 or the second main C curved member end 513 is joined to the second periodic C curved member end 519 inside of the main C curved member 501. In typical embodiments, the main C curved member 501 and the periodic C curved member 509 include about a same arc length. In some embodiments, the periodic C curved member includes about two and a half cycles of alternating C shapes (507, 508). In some embodiments, there can be more than two C shapes on the periodic C curved member 509. For example, the TriC type or TriC related structure of FIG. 10 periodic C curved member 509 includes C shaped members 1111, 1112, 1113, 1121, and 1121. In some embodiments, the periodic C curved member 509 includes about two and a half cycles of an about sinusoidal shaped curve.

In some embodiments, at least one of the main C curved member or the periodic C curved member include an additional different shape. For example, the additional different shape includes a substantially straight line.

In some embodiments, the periodic C curved member 509 includes at least one C shape 2751 which is larger in comparison to either of two smaller C shapes 507, 508 on either end of the at least one C shape. In some embodiments, at least one C shape 2751 larger than either of two smaller C shapes 507, 508 follows a path about parallel to the main C curved member. In some embodiments, the main C curved member 501 includes an arc length 501 of up to about 350 degrees arc of a full circle with periodic C curved member 509 within including at least one C shape 2753 larger than either of two smaller C shapes 507, 508 (FIG. 27C).

The Z Boom end face (cross section) structure includes two opposite substantially flat members joined from opposite sides by about an S curve member. The curve member is joined at both ends, here each curve end joined to a different flat member.

A deformable beam typically has three characteristic shapes that it can be deformed into.

In a first configuration, the deformable beam has substantial width and height in directions transverse to the longitudinal axis with an aspect ratio typically ranging from about 0.1 to 1. The width and height give the beam substantial bending stiffness and strength by providing substantial cross section moment of inertia. The configuration may also have substantial axial, shear and torsional stiffness and strength compared to the flattened state, the extended state typically has 10 to 10,000 times greater bending stiffness and strength, 10 to 1,000 times greater torsional stiffness and strength, and 10 to 10,000 greater axial strength.

In a second configuration, the deformable beam dimensions in one or more of the transverse directions are reduced to the material thickness which is typically 10 to 1000 times less than the extended transverse dimension. This reduction in transverse dimension reduces the stiffness and buckling strength of the deformable beam. The deformable beam cross section at the ends of the beam may flatten or remain un-deformed. The beam cross section near the ends of the beam can be modified (non prismatically to allow the transition from the beam end to a location within the beam such that stress concentrations and material failure are avoided. Example modifications are changes in material thickness, tapering the cross section, cutting away parts of the cross section, and adding material to the cross section.

In a third configuration, the shape of the second configuration is typically bent or rolled into the final alternate configuration of the structure. An elastic beam in bending should have surface tensile and compressive strains about equal to the ratio of the beam transverse direction perpendicular to the roll axis to the rolling diameter. Flattening the cross section reduces the material strain so that the material does not fail. The cross section dimension is typically reduced by 10 to 1000 so that the desired material strength is reduced by the same ratio.

FIG. 2A shows a cross section view of a DubC Boom. FIG. 2B shows an isometric view of an opened DubC Boom. FIG. 2C shows an isometric view of a nearly flattened DubC Boom. FIG. 2D shows an isometric view of a rolled DubC Boom.

FIG. 3A shows a cross section view of a DubC Hinge. FIG. 3B shows an isometric view of an opened DubC Hinge. FIG. 3C shows an isometric view of a flattened DubC Hinge. FIG. 3D shows an isometric view of a rolled DubC Hinge.

FIG. 4A shows a cross section view of a MidC Hinge or Beam. FIG. 4B shows an isometric view of an opened MidC Hinge. FIG. 4C shows an isometric view of a nearly flattened MidC Hinge. FIG. 4D shows an isometric view of a rolled MidC Hinge.

FIG. 5A shows a cross section view of a TriC Hinge. FIG. 5B shows an isometric view of an opened TriC Hinge. FIG. 5C shows an isometric view of a flattened TriC Hinge. FIG. 5D shows an isometric view of a rolled TriC Hinge.

FIG. 6A shows a cross section view of a TriC Flat Boom. FIG. 6B shows an isometric view of an opened TriC Flat Boom. FIG. 6C shows an isometric view of a flattened TriC Flat Boom. FIG. 6D shows an isometric view of a rolled TriC Flat Boom.

FIG. 7A shows a cross section view of a Z Boom. FIG. 7B shows an isometric view of an opened Z Boom. FIG. 7C shows an isometric view of a flattened Z Boom. FIG. 7D shows an isometric view of a rolled Z Boom.

FIG. 8A shows a cross section view of a Z Hinge. FIG. 8B shows an isometric view of an opened Z Hinge. FIG. 8C shows an isometric view of a flattened Z Hinge. FIG. 8D shows an isometric view of a rolled Z Hinge.

FIG. 9 shows another drawing showing end view cross section classes of exemplary Z Boom deformable structures.

FIG. 10 shows another drawing showing end view cross section classes of exemplary C Boom deformable structures.

FIG. 11 shows yet another drawing showing end view cross section classes of exemplary C Boom deformable structures.

FIG. 12 shows yet another drawing showing end view cross section classes of exemplary C Boom deformable structures. In the top left and bottom two cross section drawings (end view) of FIG. 12, an end face cross section of the deformable beam or hinge includes a first about V shaped member 1201 defined by a pair of first member arcs 1221, 1223 joined at a first end of each first member arc to form a first vertex 1225. A second about V shaped member 1251 is defined by a pair of second member arcs 1261, 1263 joined at a first end of each second member arc to form a second vertex 1265. A pair of substantially flat trailing sections 1262, 1264 on either side of an opposite end of each second member arc 1261, 1263, and an opposite end of each first member arc is joined to an end of each of the pair of substantially flat trailing sections at joints 1271, 1273.

In the lower two cross sections of FIG. 12, at least one of the pair of substantially flat trailing sections on either side of an opposite end of each second member arc 1281, 1283 continues past a joined section 1271, 1273 and curves towards a direction about perpendicular to an axis of the pair of substantially flat trailing sections 1262, 1264.

In the lower right side cross sections of FIG. 12, at least one of the pair of first member arcs 1221, 1223 continues past 1291, 1293 a joined section at the first vertex 1225 and curves outward towards a direction about parallel to an axis of the pair of substantially flat trailing sections.

Another way to view or conceptualize the lower cross sections of FIG. 12 is as, two angled about C shaped members joined at a vertex with the ends of the about C shaped members disposed in two about flattened C shaped members sitting side by side. In the lower right side cross sections of FIG. 12, the two angled about C shaped members can also be viewed as joined at their shoulders.

FIG. 13 shows yet another drawing showing end view cross section classes of exemplary TriC variation, DubC Variation, and other variation deformable structures.

End Modifications

In most embodiments, the strongest and the stiffest structure is obtained by mounting a deformable structure such that one or both ends of the structure do not deform, i.e. the deformable structures are mounted by any suitable mounting means (e.g. bonded, clamped, bolted, etc.) to an effectively rigid structure.

However, the transition from the deformed flattened state to an un-deformed end can result in stress and strains that are much higher than those generally occurring in the main rolled section. These stress and strain concentrations can be alleviated by tailoring the geometry of the structure at the ends and also by tailoring the geometry of the un-deformed part of the hinge (the mount region).

Examples of such end modifications are shown in the drawings of FIG. 14-FIG. 17. The modifications include 1) Cut-outs (end geometry modification, cutout lines); 2) Mount modifications (changes to the effectively rigid mounting region, rigid lines); Structures may be mounted only by the solid rigid line or over the region encompassed by the dashed rigid line; and 3) Any suitable combinations of the two modifications.

FIG. 14 shows exemplary DubC end modifications. FIG. 15 shows exemplary MidC end modifications. FIG. 16 shows exemplary TriC end modifications. FIG. 17 shows exemplary Z Boom end modifications.

Composite Laminates

Composite laminates are an example of a suitable material from which to make the deformable structures described in this Application. When fabricated from laminated fibrous (continuous or short fibers) composite materials, the fiber orientation within a ply can be tailored to achieve a better structure (stronger, stiffer, more deformable, increased dimensional stability, etc.). Also, the lamina and laminate thicknesses can be non-uniformly varied with the structure cross section to place more material where it is needed and less where it is not needed. The laminate can be modified to reduce mass, increased stiffness and strength in the extended state, reduce material stress and to enable more compact packaging in the rolled state, or to reduce stress concentrations in the ends.

Where thickness is added, the material could be a unidirectional (UD) type or balanced (B) type. The thickness variation is applicable to any material used in fabrication of the structure (e.g. metals and plastics).

The drawings of FIG. 18A to FIG. 25 show exemplary laminate configurations designed to achieve specific benefits. The 0° direction is parallel to the prismatic (long) axis on the structure (perpendicular to the plane of the cross section). The 90° direction lines with the plane of the cross section and is parallel to the laminate. Off axis directions (e.g. 45°) lie between 0° and 90° and are also parallel to the laminate.

Laminate plies are either Uni Directional (UD, all fibers in one direction) or Balanced (B, an equal number of fibers in the +θ and −θ directions). Balanced plies are readily achieved with weaves (e.g. plain weave with fibers at +45° and −45°) or with several plies of Uni Directional materials, e.g. [+θ/−θ], [+θ/−θ/+θ/−θ], and [+θ/−θ/−θ/+/74 ].

Laminates are described as: [ply 1/ply 2/ply 3/etc.] where “ply n” is either UD or B. UD is followed by the fiber direction (e.g. UD@0° to indicate a uni directional ply with fibers parallel to the long axis). “B” alone is understood to include any suitable type of balanced ply. It shall also include [0/90] woven and UD laminates and variations. Where the laminate is not symmetric, e.g. [UD@0/B], the reversed laminate is also claimed, as in [B/UD@0]. Some or all B plies may be replaced with “T” plies where T indicates the ply is continuous or short fiber textile made by braiding or weaving processes. T plies may have groups of fibers in 0, 90, +45, −45, theta, any combination of these orientations and relative quantities.

FIG. 18A and FIG. 18B show drawings of DubC structures with a laminate thickness variation across the structure. FIG. 18A shows end view of a DubC deformable structure having a thicker center relative to the tips, which provides an enhanced axial stiffness. FIG. 18B shows end view of a DubC deformable structure having thicker tips relative to the center portion, which provides an enhanced bending stiffness.

FIG. 19A-FIG. 19D show drawings of various DubC fiber orientations. FIG. 19A shows an end view of a DubC [B/UD@0/B] center, [B] ends deformable structure, which provides an enhanced axial stiffness. FIG. 19B shows an end view of a DubC [UD@0/B/UD@0] center [B] ends deformable structure, which provides an enhanced bending stiffness. FIG. 19C shows an end view of a DubC [UD@0/B/UD@0] center [B/UD@0] ends deformable structure, which provides an enhanced bending stiffness. FIG. 19D shows an end view of a DubC of substantially all [B/UD@0/B] deformable structure, which provides an enhanced torsional stiffness. FIG. 19E shows an end view of a DubC deformable structure of substantially all [UD@0/B/UD@0]. These variations show the benefits of 1) modification of the laminate stacking sequence and 2) modification of relative lamina thicknesses. Laminate stacking sequence is more uniform and easier to fabricate while modification of relative lamina thickness offers higher performance, but is more complex and difficult to fabricate.

FIG. 20A-FIG. 20B show drawings of various MidC laminate thickness variations. FIG. 20A shows a drawing of MidC deformable structure with a thicker center relative to the tips, which provides an enhanced axial stiffness. FIG. 20B shows a drawing of MidC deformable structure with thicker tips relative to the center, which provides an enhanced bending stiffness.

FIG. 21A-FIG. 21C show drawings of various MidC fiber orientations. FIG. 21A shows an end view of a MidC center member [B/UD@0/B] and curved members of [B] deformable structure, which provides an enhanced axial stiffness. FIG. 21B shows an end view of a MidC deformable structure substantially all of [B/UD@0/B], which provides an enhanced bending strength. FIG. 21C shows an end view of a MidC deformable structure, with a [B/UD@0/B] central member and curved members of [B/UD@0/B], which provides a low mass balance between stiffness and strength.

FIG. 22A-FIG. 22C show drawings of various TriC laminate thickness variations. FIG. 22A shows an end view of a TriC deformable structure with a thicker main circle portion relative to the other portions of the TriC structure. FIG. 22B shows an end view of a TriC deformable structure with noted thicker regions relative to the other portions of the TriC structure. FIG. 22C shows an end view of a TriC deformable structure with different noted thicker regions relative to the other portions of the TriC structure.

FIG. 23A-FIG. 23C show drawings of various TriC fiber orientations. FIG. 23A shows an end view of a TriC deformable structure with a [B/UD@0/B] main circle portion, where the other portions are [B], which provides an enhanced axial stiffness. FIG. 23B shows an end view of a [B] type TriC deformable structure with a [B/UD@0] main circle portion, where the other portions are [B], which provides an enhanced torsional stiffness. FIG. 23C shows an end view of a TriC deformable structure with a [B] main circle portion, where the other portions are [B/UD@0], which provides an enhanced thermal stability.

FIG. 24A-FIG. 24B show drawings of various Z Boom laminate thickness variations. FIG. 24A shows a drawing of Z Boom deformable structure with thicker flats relative to the center curved portion, which provides an enhanced axial and bending stiffness. FIG. 24B shows a drawing of Z Boom deformable structure with noted thicker regions relative to the other portions, which provides an enhanced bending stiffness with low mass.

FIG. 25 show drawings of various Z Boom fiber orientations. As shown by FIG. 25, the either or both of the flats and/or the center curved portion can included any of the [B/UD@0/B], [B/UD@0], and/or [B] fiber orientations or any combinations thereof.

Deformable structures can be made from any suitable relatively thin material that can be shaped to the desire cross section. While composite materials often provide the highest performance, they may be expensive, difficult to acquire, difficult to fabricate, or not have appropriate physical properties (strength, conductivity, density, thermal expansion) for an application. Alternate materials are relatively thin metal sheets, for example spring tempered steal, brass, aluminum, copper, nickel, titanium, and alloys containing these metals. Deformable structures can also be formed from plastic sheets, for example, polyamide, polyimide, thermosets, and thermoplastics. Beam flattened widths are typically 10 to 1,000 times the material thickness.

FIG. 27A shows a drawing of yet another exemplary TriC deformable structure with about flat sections. FIG. 27B shows a drawing of yet another exemplary TriC deformable structure with about circular sections. FIG. 27C shows a drawing of yet another exemplary TriC deformable structure with near or about circular sections. FIG. 27D shows a drawing of yet another exemplary TriC deformable structure with near or about circular sections where the about circular sections including the C sections have a main curve which instead of closing as a circle (e.g. FIG. 27B, FIG. 27C), turns out or outwards, or flares out or outwards, at either end, such as into substantially flat or straight sections 2701, 2703 in an outward direction from a center of the main C curve. In the embodiment of FIG. 27D, the periodic C curved member 509 defines at least two about C shaped curves 2707, 2708.

FIG. 28 shows yet another drawing showing end view cross section classes of exemplary TriC variation, DubC Variation, and other variation deformable structures.

Collapsible Tubular Mast (CTM)

Deformable beams can be used as mast booms which can be rolled into relatively compact forms for storage and transport. The main boom structural elements of CTM are typically roll deployed beams. Deformable hinges can also be used to fold mast booms for storage and transport.

DEFINITIONS

The various exemplary CTM which follow include perpendicular truss members called “battens” and diagonal truss members called “diagonals”. These truss members can be substantially straight in cross section (CTM end view in the mast longitudinal direction) for substantially flat walls (e.g. FIG. 29D) or include one or more curves in cross section (CTM end view in the mast longitudinal direction) for curved walls or curved truss members forming substantially flat walls.

FIG. 29A is a drawing showing an exemplary C type CTM boom 2900. The cross section of FIG. 29D shows two opposing “V” sections (each with a C curve vertex, opposing C curves 2905, 2909) joined at two seams (2902, 2911). Each V half includes a C curve and two substantially flat walls ending in curves which form the seams. At the first end of each wall, the C curves 2905, 2909 transition into each of the two walls (C curve 2905 transitions into walls 2904, 2906, and C curve 2909 transitions into walls 2908, 2910). At the other end of each of the walls opposite the Curves, the wall curves for the seams 2902, 2911. Walls 2904, 2908 curve into seam 2902, and walls 2906, 2910 curve into seam 2911.

FIG. 29B is a drawing showing a magnified view of an end of the CTM boom of FIG. 29B.

FIG. 29C is a drawing showing a magnified view of a portion of the CTM boom of FIG. 29B. FIG. 29C shows one exemplary flat wall 2906. Flat wall 2906 (See also FIG. 29D) includes a cascaded series of a truss pattern including a perpendicular truss 2920, which is perpendicular to the longitudinal direction of the CTM 2900 boom, a diagonal truss 2921 at a first truss angle, another perpendicular truss 2920, followed by a diagonal truss 2923 at a second truss angle, and so on in a repeating pattern for about the length of the CTM 2900 boom.

Each of the perpendicular truss batten 2920 is disposed about 90° to the long axis of the seam 2911. Starting from the intersection of the perpendicular truss 2920 and the diagonal truss 2921, 2923, the diagonal truss can have a truss angle of about 45°+/−35° with respect to the batten 2920. As seen in FIG. 29C, there are typically intersections of perpendicular truss and diagonal truss at both the seam 2911 and at the C curves 2905, 2909. Other suitable truss patterns can be used.

FIG. 29D is a drawing showing an end section view of the CTM boom of FIG. 29A. In this new variation of a C type CTM boom 2900, the “C” portion is reduced to relatively smaller opposing C curves 2905, 2909. On a first longitudinal half of the CTM boom 2900, C curve 2905 joins substantially flat walls 2904, 2905, and C curve 2909 joins substantially flat walls 2908, 2910. To complete the CTM structure, flat walls 2904, 2905 are joined to flat walls 2908, 2910 respectively by corresponding seams 2902, 2911. Each of the walls, 2904, 2906, 2908, and 2910, curve outward for the respective seams 2902 and 2911.

About V shaped half, a V shaped portion with at least one curve (e.g. a curved ridge, a curved ridge including two or more curves, a C shaped vertex, or a flat back C vertex) in the vertex—About V shaped half includes structures which join two walls at some angle by a vertex having at least one curve. About V shaped is distinguished from “V shaped” in that typically the vertex is not a sharp right angled ridge (however, when the structure is deployed, for example, the walls of the about V shaped half can be any suitable angle with respect to each other, including 90°).

Vertex options—FIG. 29A to FIG. 29D show a CTM boom having a C curve which extends on either side to a wall. Generally, a CTM boom has a rounded vertex, typically a C shaped vertex, or a flat back C shape which includes a flat section with curves on either side of the flat (e.g. FIG. 30, FIG. 31). Any suitable curved vertex can be used.

Another suitable exemplary alternative vertex has a flat-back C curve as the vertex. FIG. 30 shows a cross section of a CTM boom 3000 using a flat-back C curve 3005 having curves 3005 a, 3005 c and flat back 3005 b, which extends into walls 3004, 3006.

Truss patterns—FIG. 31 shows a CTM boom 3100 using a flat-back C curve 3005 with an alternative truss pattern to the trusses of FIG. 29A to FIG. 29D. The CTM boom 3100 includes successive patterns of batten 3120 and diagonal truss 3121 (similar to batten 2920 and diagonal truss 2921, FIG. 29C).

FIG. 32 shows a CTM boom 3200 using a flat-back C curve 3005 with diagonal truss 3223 on the first half “V” section (e.g. the upper section, FIG. 32) of two opposing V sections and different angles of diagonal truss 3221 on the second half V section (e.g. the lower section, FIG. 32) and perpendicular truss 3220. The different angles can be similar to the different diagonal trusses 2921, 2923 of FIG. 29C.

FIG. 31 and FIG. 32 have the same lacing pattern. In FIG. 31 and FIG. 32, the direction of the bottom diagonals is reversed relative to the top.

FIG. 33 shows a CTM boom 3300 using a flat-back C curve 3005 with diagonal truss 3323 with angles shallower compared with the previous exemplary diagonal trusses. Each of the perpendicular truss 3320 is disposed about 90° to the long axis of the seam 3311. Starting from the intersection of the batten 3320 and the diagonal truss 3323, the diagonal truss can have a truss angle of about 45°+/−35° with respect to the batten 3320. Similar to the CTM boom 2900 of FIG. 29C, there are typically intersections of perpendicular truss and diagonal truss at both the seam 3311 and at the flat back C curves 3005. Other suitable truss patterns can be used. Note that the exemplary FIG. 33 lacing is different from the exemplary CTM structures of FIG. 31 and FIG. 32. In FIG. 33, the top and bottom diagonals are in the same direction (parallel to each other).

FIG. 34 shows a CTM boom 3400 using a flat-back C curve 3005 with diagonal truss similar to the CTM boom 2900 of FIG. 29A to FIG. 29D, however using shallower angle diagonal truss 3421, 3423 similar to diagonal truss 3221, 3223 of FIG. 32. Note that the exemplary CTM of FIG. 34 is different from previously described exemplary CTM structures. Here, the diagonal directions alternate in each cascading bay and are parallel on the top and bottom.

FIG. 35 shows a top view of the CTM boom 3400 of FIG. 34.

Fiber orientation—As described hereinabove, fiber orientation can be used to further strengthen a CTM boom. For example, the lines 3160 show fiber patterns parallel to each member axis in FIG. 31.

Yet another exemplary CTM includes a configuration is where the alternating diagonals of FIG. 34 are not parallel on the top and bottom, but they are reversed as shown in FIG. 31 and FIG. 32.

Battens and Diagonal Truss Members

In the exemplary CTM hereinabove, the walls are all show as flat. However, the walls can also have any suitable curve in cross section. For example, the walls can be curved with a C curve, or the individual truss members can be curved such as is used in a tape spring. For example, the cross sections of members 2920, 2923, 2921 can be curved like a tape spring, with relatively flat C shape.

Curved Truss Members (Battens and/or Diagonals)

Either or both of one or more battens, or diagonals, can be curved truss members of a substantially flat CTM boom wall.

FIG. 42 is a drawing showing an exemplary curved truss member, curved in a way analogous to a tape spring or tape measure. However, the exemplary curved member of FIG. 42 transitions at either end to a flat portion 4201 a, 4201 b to mechanically couple to the vertex portion and the joined sections respectively. FIG. 43 is a drawing showing a mid-section cut-away of the curved truss member of FIG. 42. FIG. 44 is a drawing showing an end view of the sectional cut-away of FIG. 43.

FIG. 45 is a drawing showing an exemplary CTM boom 4500 using curved diagonal truss members 4200. It is unimportant whether the flat portions 4201 a, 4201 b (FIG. 42) are about perpendicular at the ends to the longitudinal axis of the diagonal truss member, or if the flat portions 4201 a, 4201 b are angled according to the angle of the diagonal to match the longitudinal axis of the vertex, a flat back C curve in FIG. 45, and/or joined portions of the CTM boom 4500. FIG. 46 is a drawing showing a cross section view of the CTM boom 4500 of FIG. 45. This end view drawing of the boom is analogous to FIG. 29D.

Strut Lacing

In the exemplary CTM hereinabove, the walls typically include a combination of battens and diagonal members (both forward diagonal and reverse diagonal). However, there can also be CTM structure with only diagonal members (same direction, or multiple direction), or CTM structures with only battens. Strut lacing of the truss can include any combination of battens or diagonals, or combinations thereof.

Applications of CTM Booms

In one exemplary application of a CTM boom, the CTM boom can be used to deploy a relatively large solar panel in space, such as can be used of space to terrestrial power generation. In terrestrial power generation, sunlight is converted to electrical power by panels deployed in geostationary orbit around the Earth. The electrical power is then beamed to Earth, such as by microwave electromagnetic radiation. One advantage of such power stations is that the solar panels are always irradiated during daytime hours, regardless of cloud conditions over the terrestrial receiving station. The new CTM boom is ideal for deploying and supporting such relatively large solar panels in space. While there are only relatively small gravitational forces on the deployed panels in the “weightlessness” of space, the truss patterns are important both to opening a folded CTM into the cross section of FIG. 29D, as well as to maintain the structural integrity of the CTM boom experiencing mechanical forces while deploying a solar panel mounted to each CTM, mechanical forces associated with acceleration of the satellite or spacecraft.

The exemplary CTM boom 2900 as implemented for space based solar panels or solar arrays is about 40 m long (about 131 feet) and has a mass of about 29.8 kg (about 65 lbs). Once opened from a flattened state, the cross section (FIG. 29D) has an effective diameter of about 0.4 m.

Solar panels can be supported and deployed by any suitable CTM means. For example, there can be a solar panel assembly or solar array at the end of any of the exemplary new CTM structures described hereinabove. Also, the new CTM structures described hereinabove can be used to deploy solar panels or solar array along the length of the CTM. For example, any of the newly described CTM can be used to deploy an accordion or other style folded solar array or solar panels.

Particularly as solar arrays and other planar devices (e.g. planar antennas, phased array antennas, reflectors, and reflector arrays) become larger, another application for the various exemplary CTMs described hereinabove is to deploy four CTM to create a space based frame which can support any relatively large about planar device within the CTM frame.

CTM Frames for Planar Devices (Flat, Convex, or Concave)

FIG. 36 is a drawing showing an isometric view of exemplary four sided CTM frame 3600 (CTMs shown as solid legs for simplicity, any of the new CTM structures described hereinabove can be used for such frames as shown in FIG. 36 to FIG. 38). There can be corner sections 3603 mechanically mounted to the corners. The frame of FIG. 36 is especially useful for space based applications of solar sails, solar arrays, solar panels, planar antennas, phased array antennas, reflectors, and reflector arrays, combinations thereof, etc.

FIG. 37 is a drawing showing a top view of the CTM frame 3600 of FIG. 36.

FIG. 38 is another top view of a variation of a CTM frame 3800 similar to FIG. 36 showing in addition to corner sections 3603, there can be a supporting sheet material 3805 which ultimately supports either underneath or at the sides a square payload 3899. Square payload 3899 can include, for example, solar sails, solar arrays, solar panels, planar antennas, phased array antennas, reflectors, and reflector arrays, combinations thereof, etc.

Frames similar the exemplary CTM frames of FIG. 36 to FIG. 38 can be made using any suitable deformable boom, such as including other types of booms described hereinabove.

Similar frames based on any suitable booms described hereinabove and combinations thereof, to support a planar (flat, concave, or convex) solar sail, solar array, solar panels, reflectors, antennas, solar sails, etc., can be made as a four sided frame as per the exemplary frames of FIG. 36-FIG. 38. Other frames can be made to support planar devices, planar sheets, either flat, convex, or concave, including 3 booms for a triangular planer device, or more than 4 booms using any suitable number of booms for polygon shape. Similarly, frames need not be square, and suitable frame shapes include, for example, trapezoid, triangle or trigon, quadrilateral or tetragon, parallelogram, square, rectangle, rhombus, pentagon, hexagon, heptagon, octagon, enneagon, decagon, hendecagon, dodecagon, triskaidecagon or tridecagon, tetrakaidecagon or tetradecagon, pendedecagon, hexdecagon, heptdecagon, etc. A relatively large number of booms can also be used to approximate a circle or ellipse.

Alternative frame types can also be used, such as, for example, including an H configuration, a radial 3 configuration, and a radial 4 configuration.

FIG. 39 is a drawing showing an exemplary frame based on a H configuration architecture.

FIG. 40 is a drawing showing an exemplary frame based on a radial 3 configuration architecture.

FIG. 41 is a drawing showing an exemplary frame based on a radial 4 configuration architecture.

Corner supports as described hereinabove can be used with any type of frames. Supports, supporting layers, or underlying planar layers can be used to deploy planar devices of different shapes on or within such supports, supporting layers, or underlying planar layers. Any of the planar layers described hereinabove can be about flat, substantially flat, concave or convex. There can also be any combinations thereof (of about flat, substantially flat, concave or convex) within one planer device or an array of planar devices. Such planar device can also include ridges, troughs, wrinkles, and combinations thereof.

Any intersections of such frames can be hinged, such as by use of any of the hinges described hereinabove, such as, typically for pre-deployment storage and shipping, including shipping by rocket or spacecraft. Any sections of such frames can also be hinged to fold for compact storage and/or shipping.

Frames with Hinges

Any of the frames described hereinabove can also use hinged joints including any suitable hinge, such as, for example, any suitable hinge described hereinabove.

CTM booms can be used to deploy any suitable relatively high mass payload and are not limited to deploying solar panels or solar arrays in space based applications.

Materials and fibers—Any the suitable boom materials, including fiber patterns, described hereinabove, can be used to make CTM booms. For example, the seam areas can be reinforced or strengthened by a different fiber pattern as shown by the thicker regions of FIG. 22B (2231), or by FIG. 24B, where seams are shown to include thicker regions.

Methods of Manufacture—A new method of manufacture for CTM beams is described by co-pending U.S. patent application Ser. No. ______, which application is applications is incorporated herein by reference in its entirety for all purposes.

Any of the deformable structures can be made to have less mass (“light weighted”) by cutting out or otherwise removing sections along the length of one or more of the members of a beam (including booms) or hinge. Any suitable number of any suitable sized cutouts can be used. Any suitable cutout shape can be used, such as, for example, circular shape, elliptical shape, square shape, rectangular shape, triangular shape, trapezoid shape, polygon shape, etc.

All of the optional properties, such as, material composition, fiber orientation, and member thickness apply in any combination thereof to all of the described deformable structures.

Deformable structures can be fabricated from any process that can achieve the desired cross section. Example continuous processes include extrusion, pultrusion, pulwinding, pulbraiding, etc. These processes can involve fibrous materials, bulk materials, and any combination thereof. Example fixed length processes include milling, molding, and thermoforming. Deformable structures can be injection molded, bladder molded, roll wrapped, open molded, closed molded, resin transfer molded, vacuum assisted resin transfer molded, formed using sheet molding compounds. Cross section pieces can be made independently by any of the above processes and later joined by any of several joining processes including bonding, welding, fastening, and interlocking.

According to one aspect, an apparatus includes at least one or more deformable structure of the type DubC Boom, DubC Hinge, MidC, TriC Boom, TriC Hinge, Z Boom, Z Hinge, and any cross section combinations thereof. The at least one or more deformable structure optionally includes one or more end modifications. The at least one or more deformable structure optionally includes a composite laminate. The at least one or more deformable structure can be used in one or more of the following: Suspension flexures (wheels, mountain bikes, road bikes, ATVs, etc.), Tape measures, Hinges, booms, beams, masts, Hinges/structures for unfolding consumer products: display assemblies, shades, Photography screens and shades, Umbrella and parasols, Tents, Cots, beds, stretchers, Ladders (hunting, photography, wildlife observation, fishing), Folding Beams/poles to push/pull with, anchor with, support cameras and sensors, above and under water, Antennas (Wi-Fi, Radio, cell phone, RF, TV, satellite phone/tv), Backpacks, Springs (leaf, tension, compression, torsion, etc.), Wagons, strollers, chairs, Sun shades, awnings, retractable roofs, Replace mechanical (pin-clevis) hinges, Replace telescoping tubes, Unfolding containers (boxes and bags), Flexure hinges for precision positioning systems, Sealed hinges, Orthotics and prosthetics, Control surface actuator hinges, Compliant mechanisms (morphing structures), Deployable space and terrestrial antennas, Deployable space booms, Deployable space structures (tape-spring structures and solar arrays, solar sails), Deployable wings and airfoils, Parafoils, parafoils stiffeners, parachute deployment device, Deployable atmospheric decelerators, shallow water anchors, and, Medical braces and splints.

It will be appreciated that variants of the above-disclosed and other features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the following claims. 

What is claimed is:
 1. A deformable device comprising: a deformable beam or hinge having an extended state, a flattened state, and a rolled state if a beam, where a stiffness and strength of the deformable beam or the hinge in the extended state is greater than a different stiffness and strength of the deformable beam or the hinge in the flattened state, said deformable beam or the hinge deformable along a long axis; an end face cross section of said deformable beam or the hinge transverse to said long axis comprising: a first periodic curved member defining at least two shaped curves, said first periodic curved member comprising a first arc length; and a second periodic curved member defining at least two shaped curves, said second periodic curved member comprising a second arc length, said second periodic curved member mechanically coupled to said first periodic curved member at respective ends of said end face cross section; and wherein said first arc length and said second arc length are of about a same arc length.
 2. The deformable device of claim 1, wherein said first arc length and said second arc length are of a substantially same arc length.
 3. The deformable device of claim 1, wherein said first arc length and said second arc length comprise a substantially same arc length between both joined curve ends.
 4. The deformable device of claim 1, wherein said first arc length and said second arc length comprise a substantially same arc length between both joined curve ends of said end face cross section.
 5. The deformable device of claim 1, wherein said first periodic curved member comprises at least two about C curved members.
 6. The deformable device of claim 1, wherein said second periodic curved member comprises at least two about C curved members.
 7. The deformable device of claim 1, wherein said first periodic curved member comprises at least two about C curved members and said second period curved member comprises at least two about C curved members.
 8. The deformable device of claim 1, wherein at least one of said first periodic curved member and said second periodic curved member comprise an additional different shape.
 9. The deformable device of claim 1, wherein at least one of said first periodic curved member and said second periodic curved member comprises a [B/UD@0/B] fibre structure or a [B/UD@0] or a [B] fibre structure.
 10. The deformable device of claim 1, wherein at least one member of said deformable device comprises at least one cut out along a length of said member.
 11. The deformable device of claim 1, wherein said first periodic curved member comprises a different thickness relative to said second periodic curved member.
 12. The deformable device of claim 1, wherein at least one of said first periodic curved member and said second periodic curved member comprises a variation in thickness across either or both of said first periodic curved member and said second periodic curved member. 